2012
Ind. Eng. Chem. Res. 1990,29, 2012-2020
Higgin, J. B.; Lappierre, R. B.; Schlenker, J. L.; Rohrman, A. C.; Wood, J. D.; Kerr, G. T.; Rohrbaugh, W. J. The Framework Topology of Zeolite Beta. Zeolites 1988, 8, 446-452. Inoue, T.; Sato, M. Conversion of Aromatic Hydrocarbons with Zeolite Catalysts (Part I) Transalkylation of Toluene and Trimethylbenzene on Synthetic Zeolite Catalysts. J . J p n . Petrol. Inst. 1981, 24 (2), 136-141. Kaeding, W. W.; Chu, C.; Young, L. B.; Butter, S. A. Shape-Selective Reactions with Zeolite Catalysts 11. Selective Disproportionation of Toluene to Produce Benzene and pXylene. J . Catal. 1981,69, 392-398.
Meisel, S. L.; McCullough, J. P.; Lechthaler, C. H.; Weisz, P. B. Gasoline from Methanol in One Step. CHEMTECH 1976,86-89. Mikhail, S.; Ayoub, S. M.; Barakat, Y. Conversion of Trimethyl-
benzene over Y-Zeolite Catalyst. Zeolites 1987, 7, 231-234. Waldinger, R. L.; Kerr, G. T.; Rosinki, E. J. Catalytic Composition of A Crystalline Zeolite. US Patent 3,308,069, 1967. Wu, J. C.; Leu, L. J. Toluene Disproportionation and Transalkylation Reaction over Mordenite Zeolite Catalysts. Appl. Cat a l . 1983, 7, 283-294.
Yang, H. M.; KO, J. W.; Wu, J. Unpublished data, 1984. Yashima, T.; Matsuoka, Y.; Maeshima, T.; Hara, N. Transalkylation of Toluene with Trimethylbenzene on synthetic Zeolites. J . Jpn. Petrol. Inst. 1972, 15, 487-492. Received for review December 4, 1989 Revised manuscript received May 15, 1990 Accepted May 23, 1990
Wiped Film Reactor Model for Nylon 6,6 Polymerization David D. Steppan,+Michael F. Doherty,’ and Michael F. Malone*’$ Department of Polymer Science and Engineering a n d Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
A wiped film model for the design and performance analysis of continuously mixed thin-film nylon 6,6 polymerizers has been developed. The description is based on composition-dependent rate and equilibrium constants, a realistic degradation scheme, and finite gas-phase condensate concentrations. Even small amounts of mixing yield very large improvements in both the mass transfer and molecular weight generation in a wiped film reactor. Nylon 6,6 degradation reactions reduce the molecular weight generation by about 15% under typical operating conditions. These wiped film reactors should be operated between 280 and 285 “C and a t low pressure (5300mmHg) in order to achieve maximum molecular weight and good product quality with the smallest reactor. Higher temperatures severely affect the product quality through degradation, and increasing the pressure lowers the maximum attainable molecular weight. A catalyst for the main amidation reaction could yield improved reactor performance a t all but the lowest mixing rates. Introduction The “finishing” stage of continuous polycondensation largely determines the final product molecular weight and “quality”. Other investigators have attempted to formulate realistic process models for this important operation. For example, Ault and Mellichamp (1972a-c) developed a “periodically mixed” film model in which they assumed that a stationary polymer film was laid down and subsequent polymerization and mass transfer occured for a certain exposure time, after which the film was instantaneously well-mixed and the process repeated. They used a simplified kinetic model that included no side reactions or degradation reactions and ignored any diffusional resistance at the gas-film interface. Another model for wiped film polymerization reactors was developed by Amon and Denson (1980, 1983). They assumed that only a fraction of the material was laid down in the well-mixed film while the majority remained in a bulk pool adjacent to the moving wiper blade. The reaction was assumed to occur only in the bulk and condensate removal only in the film. They approximated the film thickness as infinite as far as mass transfer was concerned and, consequently, did not investigate the effect of film thickness. In addition, they also used a simplified kinetic model that did not include any side or degradation reactions. Gupta et al. (1983) modified the model of Amon and Denson to include the effect of film thickness. They compared the model of Ault and Mellichamp to that of Department of Polymer Science and Engineering. *Department of Chemical Engineering.
0888-5885/90/2629-2012$02.50/0
Table I. Nylon 6,6 Reactions C-SE+W degradation L-SE+A SE COz + SB SB + 2A X t 2NH, polyamidation A+C L+W
- -
1.1 1.2 1.3 1.4
1.5
Amon and Denson and found the two models gave nearly identical predictions. More recently, Kumar et al. (1984) studied the finishing stage of poly(ethy1ene terephthalate) (PET) polymerization with this modified Amon and Denson model and a kinetic scheme that included reactions with monofunctional compounds as well as redistribution and cyclization reactions. The finishing stages of PET polymerization have also been studied by Ravindranath and Mashelkar (1984) with the mixing film model similar to that of Ault and Mellichamp. However, they included degradation reactions in their kinetic scheme as well as an “effective flashing” technique to account for a changing interfacial concentration. A wiped film model for the design and performance analysis of continuously mixed thin-film nylon 6,6 polymerizers will be developed. Realistic kinetic and equilibrium correlations as well as a degradation scheme (Steppan et al., 1987, 1990b) will be used. The model predictions will be compared to the results of Kumar et al. (1984) and Ravindranath and Mashelkar (1984) for PET. The comparison is especially interesting since PET and nylon 6,6 have very different equilibrium constants (about unity versus several hundred) and degradation reactions. We will use a mixing film model similar to that of Ault and Mellichamp. However, we will assume a plug flow velocity profile in the film, which enables us to relate a 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2013 Table 11. Kinetic Parameters for Nylon 6,6 Degradation reaction rate constant ko, l / h E,,,, cal/mol To,"C 293 0.06 30 OOO 1 kl 305 0.005 30000 2 k2 30 000 305 2 k2c 0.32 10 000 305 a = 0.1 3 k3 0.35 50 000 305 b = 0.3 10.0 4 k4
reaction time to a residence time and ultimately to a reactor size. We do not employ the effective flashing technique of Ravindranath and Malshelkar primarily because it requires knowledge of the compositional variation of the Flory (1953) x parameter or the assumption that it is constant. There is strong evidence that the latter is unrealistic in these polar condensation systems (Costa, 1983). We will use a correlation of experimental data to describe the interfacial concentration, as described below.
Nylon 6,6 Polymerization The main amidation reaction and degradation model are summarized in Table I (Steppan et al., 1990b) where SE refers to a cyclic or stabilized end group, C 0 2 refers to carbon dioxide, SB refers to a Schiff base, and X refers to a cross-linked compound. The reaction rates of the proposed degradation model (reactions 1.1-1.5) are given by R1 R2
(1)
CTklXc
= CTXL(k2
+ k2cXA)
(2)
Gas-FiIm Interface (Z= HI
3I
Direction of ,Mixing Blade
Outlet Inlet
Z
(b)
Figure 1. Schematic diagram of the wiped film reactor.
The water balance for the flowing film model is (see Steppan et al. (1989))
I
R5
= CTkapp(
XAXC
T)
- XLXW
(5)
where C T = CA + Cc + C L + Cw + CSE + CSB + Cx, and X A = C A / C T , etc. The temperature dependence of the rate constants was fit with an Arrhenius form. 12 = ko exp(
?[f k]) -
\
(6)
The kinetic parameters for reactions 1.1-1.4 are shown in Table I1 (Steppan et al., 1990b). The apparent rate and equilibrium constants in eq 5 are complicated but known functions of temperature and composition given by Steppan et al. (1987).
Wiped Film Model A cross section of a wiped film reactor is shown in Figure la. The blades are pitched at some angle with respect to the axis of rotation to convect the polymer through the device in addition to mixing the film. The mean residence time is a function of both the pitch angle and the rotation rate of the blades. The actual flow field is a complex three-dimensional flow. However, it must have a fairly narrow residence time distribution to produce high-quality polymer since nylon 6,6 undergoes rather rapid degradation at these elevated temperatures. Keeping this in mind, we have adopted a simplified wiped film reactor model geometry (Figure lb). Water diffuses out of the film toward the gas-film interface (in the Z direction), and the reacting polymer flows through the reactor in the Y direction. By assumption, there are no variations in the X direction.
The variables in the model have been scaled with respect to a characteristic time, length, concentration, reaction rate constant, and velocity. We have chosen the characteristic time as the ratio of the square of the film thickness to the diffusivity ( P / D ) ,where the diffusivity is taken at the temperature of the system. The characteristic length is taken to be the film height (H),and the characteristic concentration is the initial value for water (C&) entering the reactor. For the characteristic reaction rate constant, we use the value of the main amidation reaction at 200 "C as both the water and carboxyl end group mole fractions approach zero (k:pp = 2.926/h). The characteristicvelocity is the film average velocity ( u y ) . This is an isothermal model, which is a good assumption for the thin films found in these devices. In eq 7, Cw is the water_concentration,x = Cw/c is the mole fraction of water, C = C A + Cp is the total molar concentration (Cp is the polymer concentration), rw is the rate of water production, and uy is the fluid velocity is the flow direction. In deriving eq 7, we have assumed that the reacting mixture can be treated as a binary solution for diffusion (pseudobinary approximation), that the mutual diffusivity depends only on temperature but not on composition, that the polymer does not diffuse in the 2 direction, that water diffuses in the 2 direction, and that axial diffusion is negligible compared to convection in the Y direction. The Damkohler number (Da) can be defined as (e.g., Lin and Van Ness, 1973)
/ ( Y ) =-hesideme Da = 1/k&p treaction
(8)
2014 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
where ( u y ) and L are the average velocity and the axial length of the film. The Thiele modulus (@) is (e.g., Smith, 1970)
where H is the film thickness and D the mutual diffusivity of the water-polymer mixture. Under constant reaction conditions (temperature and catalyst concentration), it is useful to interpret increasing the Damkohler number as increasing the residence time or reactor length and increasing the Thiele modulus as increasing the film thickness. Since we are assuming a plug flow velocity profile, the reaction time of a material element and its position are not independent, and it is simple to show that
Dtl t=-Y 4z
05Y51
Table 111. Typical Values of the Thiele Modulus H,cm P / D , m i n bz H,cm R I D , min 0.2 2 0.1 1.2 100 10 0.5 1.7 200 0.4 5.5 2000 0.75 40 1.8
@*
5.0 10 100
interface, and at th_ew@(Z = 0 ) ,we assume that the flux of water is zero ( N = 0 ) or equivalently dx/aZ = 0. We assume that the film is mixed after a certain exposure time and represent the amount of mixing as the number of times the film is mixed in one residence time. The residence time (dimensionless) is given by
The number of times the film is mixed per residence time, NmiX, is given by
N m u. =- residence t exposure
It can be seen from eq 7 that Cw = Cw( Y,Z,t). The chain rule yields
Subsequent substitution for dY by differentiating eq 10, taking the partial derivative with respect to time at constant 2, and substituting eq 7 for (aCw/dt)ly,z yields
Equation 12 is identical with the stationary film model equation for water (Steppan et al., 1990a). Thus, if we move with the velocity of the plug flow, the water evolution is identical with the stationary film case. However, at a given film thickness (Thiele modulus), any value of time corresponds to a single residence time or Damkohler number (see eq 10). This is important since we are solving the evolution equations by the method of lines (Press, et al., 1986) and eq 7 requires integration in two spatial dimensions while eq 12 needs only one. The evolution equations for the various components, in dimensionless terms, are
-aCA - - 42(r, - 2r4 - r5) at
(17)
where t = The boundary conditions for the water concentration are identical with those used in the stationary film model. Thus, Cw is constant at the gas-film
(21)
where tis the exposure time (dimensionless) between consecutive mixings of the film (note, N- = 1corresponds to nonmixing operation). In a given wiped film device, the residence time and the number of mixings per residence time are not independent. In order to keep the mean residence time constant while increasing or decreasing the amount of mixing requires changing the axial pitch of the rotating blades. It is this pitch that determines how far the polymer is pushed down the device for each blade rotation (mixing). Ogata (1960) has shown that Henry's law is valid at the low water concentrations in the wiped film reactor. We will use his correlation to relate the equilibrium concentration of water at the gas-film interface to the partial pressure of steam in the gas phase.
c ~= 2cT~(103050~~-~0~09) , ~ ~ ~
(22)
In this expression, temperature is in degrees Kelvin and pressure in " H g . This differs from the effective flashing technique of Ravindranath and Mashelkar (1984) because we do not allow the interfacial concentration to change during the condensation. It is fixed by the steam vapor pressure in the reactor. Results and Discussion The Thiele modulus is proportional to the characteristic reaction time (value of the reference reaction rate constant) and also depends on the system temperature through the diffusivity. We have chosen k:pp to be 2.926/h, the value of the rate constant as the water and amine end group concentrations approach zero at 200 "C, and we have estimated the diffusivity of water in molten nylon 6,6 as 2.5 X cm2/s at 265 "C (Nagasubramanian and Reimschuessel, 1973). This diffusivity is for water in nylon 6 melts, but we expect the value to be similar for nylon 6,6 systems due the chemical similarity of the two systems. Typical values of the Thiele modulus for nylon 6,6 range from 0.1 to 10, which correspond to f i thicknesses of 0.2 to 1.7 cm (see Table 111). If we had chosen 240 "C as our reference temperature for k:pp, the Thiele modulus would range from 0.6 to 60 for the same values of H and H I D in Table III. Furthermore, if we assume that the diffusivity has a typical activation energy of 10 kcal/mol (e.g., Newitt and Weale, 1948),the film thicknesses in Table I11 would increase by one-third at 300 "C (i.e., they would range from 0.27 to 7.3 cm for the same range of Thiele moduli). This value of the diffusivity differs significantly from a value
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2015 Table IV. Typical Values of the Damkohler Number L l ( v v ) . min Da L l ( u v ) ,min Da 1 0.05 100 5.0 10 0.5 1000 50 50 2.5
of 5.0 X lo4 cm2/s reported by Roos (1974). This value would yield a range of film thicknesses from 0.02 to 0.8 cm for the values of the Thiele modulus in Table 111. Clearly, there is a need to determine the correct value of the mutual diffusivity. The value of the Damkohler number depends directly on the characteristic reaction time and on the mean residence time (L/(uy)). The Damkohler number is independent of the system temperature, and typical values are given in Table IV. We have assumed that the feed to the wiped film reactor is an equilibrium polymer-water mixture with a number-average degree of polymerization of 55 (M,i= 6200 g/mol). The feed composition and operating conditions of the wiped film reactor were estimated from a patent for continuous polyamide polymerization (US. Patent 3,900,450, 1975) and the flowing film model results of Steppan et al. (1989). We have approximated the polymer concentration by
This expression is approximate, since it is only exact provided there is a t most one cross-link per polymer molecule. Therefore, it is accurate for small amounts of cross-linking. The model predictions are computer-generated contour plots from an underlying matrix of 30 points that are the exact predictions of the model. The plotting contour routine was set up to force the contours exactly through these underlying data points rather than forming the smoothest contours. Therefore, the sometimes rather sharp contour turns reflect this choice and are not the artifact of the model assumptions, kinetic parameter uncertainties, or integration error. It is also important to realize that the contour plot is a representation of a three-dimensional surface. Therefore, if a plot has widely space contours (even with some wiggles), it is an indication of a flat and smooth surface rather than a jagged, rapidly changing one. Finally, the contour interval was kept constant for each variable across reactor conditions to allow ready comparison. In fact, the contour density provides an easy way to ''seen the sensitivity of product properties as a function of the model variables. These points should be kept in mind when viewing the results. The number-average molecular weight predictions of the model at 280 "C, 300 mmHg of steam, and nonmixing case (Nmix of unity) are shown in Figure 2a. The molecular weight is a strong function of the film thickness (Thiele modulus), and higher molecular weights can only be achieved with thin films (low Thiele moduli) without mixing. If Nmixis increased to 10 a t the same operating conditions, the effect of film thickness is diminished as shown in Figure 2b; the molecular weight production, particularly for thicker films (higher Thiele moduli), is enhanced considerably. This trend continues as we increase Nmix to 50 and 300 as shown in parts c and d of Figure 2. As Nmi,becomes very large, the effect of film thickness becomes negligible (as it should for such wellstirred systems), and the molecular weight depends only on the residence time. It is interesting to note that the point where the molecular weight contours intersect the abscissa in all these plots remains essentially constant.
4
6.7 5.6 2 4.5
r, 4.5
2.3 1.2 0.10 0.65 1.25 1.54 2.42 3.00
2.3 1.2 n -. .i 0.10 0.65 1.25 1.54 2.42 3.00
Damkohler Number
Damkohler Number
(a)
(C)
01
10.0 8.9 7.8 In j 6.7 5.6 - 4.5 3.4 + 2.3 1.2
10.0 8.9 7.8 w 6.7 5.6 - 4.5 g 3.4 I2.3 1.2
5
z
z
2 s
".
n i
01
010 065 125 154 242 300
010 065 125 154 242 300
Damkohler Number
Damkohler Number
(b)
(d)
Figure 2. Number-average molecular weight predictions for the nylon 6,6 wiped film reactor model at 280 O C and 300 mmHg steam vapor pressure: (a) N, = 1, (b) N,,, = 5, (c) N,,, = 10, (d) N,, = 50, (e) N,,, = 100, (0 N,,, = 300.
Therefore, a film thickness of about 0.2 cm (a Thiele modulus of 0.1) represents the reaction-controlled limit for molecular weight production of nylon 6,6 at this temperature. We conclude that for very thin films it does not matter whether the film is mixed or not since mass transfer is fast and the process proceeds under reaction control. However, as the film thickness (Thiele modulus) is increased, the diffusion time increases slowing the mass transfer. By mixing the film, we speed up the mass transfer, and if the mixing rate is high enough, the process can approach the rate-limiting, reaction-controlled, thin film limit. These effects have been seen previously by both Ault and Mellichamp (1972a-c) and Ravindranath and Mashelkar (1984). Kumar et al. (1984) also found that increasing the amount of mixing in the reactor increases the outlet molecular weight. However, they found the molecular weight increases as the film thickness is increased, which is exactly opposite of our results. This is a consequence of their model for the process. They use the model of Amon and Denson (1980) where the polymer film and bulk pool are separate. Mass transfer occurs only in the polymer film. Therefore, when the film thickness is increased, more polymer is in the polymer film where mass transfer occurs and less remains in the bulk pool where it does not. We have also investigated the effect of pressure, which affects the interfacial concentration through eq 22. The model predictions for a steam pressure of 100 mmHg are shown in Figure 3a and can be compared to Figure 2c, which is a t 300 mmHg and identical operating conditions. The molecular weight predictions are similar for short residence times (Damkohler numbers less than 1). However, as the residence time is increased, the lower operating pressure (100 mmHg) results in a significantly higher outlet molecular weight (by about 2000 g/mol). If the operating pressure is increased to atmospheric (see Figure 3b), the molecular weight predictions are reduced significantly compared to those a t 100 mmHg. The reason for this (pointed out by Ravindranath and Mashelkar (1984)) is that the film is reaching equilibrium for the main ami-
2016 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
0.10 0.65 1.25 1.54 2.42 3.00 Damkohler Number (a) 0 10
0.65
125
154
242
300
Damkohler Number (a)
".
,
0.10 0.65 1.25 1.54 2.42 3.00 Damkohler Number
(b)
010
065
125
154
242
300
Damkohler Number (b)
Figure 3. Number-average molecular weight predictions for the nylon 6,6 wiped film reactor model at 280 "C and Nmlx= 50; (a) P = 100 mmHg, (b) P = 760 mmHg.
dation. Higher operating pressures (and higher interfacial concentrations) reach equilibrium more quickly and therefore have reduced molecular weight a t longer residence times (Damkohler numbers) than lower operating pressures. An assumption of an interfacial concentration of zero is unrealistic, particularly for longer residence times, because this equilibrium limit can never be reached and the molecular weight will climb indefinitely toward infinity (at least if degradation reactions are ignored). The reactor temperature is another important operating variable. One has to keep in mind that it not only affects the rate of the main amidation but also the diffusion time through the temperature dependence of the diffusivity and, in addition, the melt viscosity (and therefore the energy required to mix the film) and the product quality through the temperature dependence of the degradation reactions. Figure 4a shows the molecular weight predictions for a reactor temperature of 270 "C and should be compared to Figure 2c, which is at 280 "C and identical operating conditions. The higher temperature leads to a larger molecular weight over the entire range of operating conditions. At longer residence times, an increase in molecular weight of about 1000 g/mol is typical. If the reactor temperature is increased to 290 "C as shown in Figure 4b, we can see that at low Damkohler numbers of residence times the increase in molecular is about the same as going from 270 to 280 "C. However, the improvement for thicker films (higher Thiele modulus) and longer residence times (higher Damkohler numbers) is small (the upper right-hand corners of Figures 2c and 4b are nearly identical). As the operating temperature is increased further to 300 "C, the molecular weight begins to decrease for a large portion of the operating conditions investigated, as shown in Figure 4c. Furthermore, if one
0.10 0.65 1.25 1.54 2.42 3.00 Damkohler Number (C)
Figure 4. Number-average molecular weight predictions for the = 50 and a steam vapor nylon 6,6 wiped film reactor model at Nmix pressure of 300 mmHg; (a) 270 "C, (b) 290 "C, (c) 300 'C.
interprets increasing the Damkohler number as increasing the residence time, it may be seen that the molecular weight would go through a maximum if the reactor were operated at 300 "C and a Thiele modulus of less than 2.5. In addition, if one compares the three figures (4a-c), there is also a maximum in the molecular weight production with respect to temperature at 290 "C. Both of these maxima can be attributed to the increasing effect of degradation reactions at longer reaction times and higher temperatures (faster reaction rates). At these relatively high molecular weights, stoichiometric imbalances and chain ends incapable of reaction (see reactions 1.1and 1.2 of Table I) limit the rate of molecular weight increase and eventually cause it to decrease. This type of behavior was observed by Ravindranath and Mashelkar (1984). Kumar et al. (1984) found that the molecular weight always increased as the reactor temperature was increased. However, they did find that the amount of cyclized material also increased dramatically. It should be noted that the kinetic scheme of Ravindranath and Mashelkar (1984) contains a comprehensive kinetic scheme (eight reactions) that predicts a stoichiometric imbalance that increases with time and causes a decrease in molecular weight at elevated temperatures. In contrast, the kinetic scheme of Kumar et al. (1984) is much simpler (four reactions) and contains two completely different reactions that limit the molecular weight (reactions with
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2017
1
3.00
0.10
0.65
1.25
1.54
2.42
3.00
0.10
0.65
1.25
1.54
Damkohler Number
Damkohler Number
(a)
(a)
2.42
10.0
10.0
0.9 7.0
-2a
6.7
P
f 5.6
: 4.5 E
%
4.5
+ 3.4
3.4
2.3
2.3
1.2
1.2
0.1 0.10
0.65
1.25
1.54
2.42
3.00
Damkohler Number ( b)
0.1 0.10
0.65
1.25
1.54
2.42
3.00
Damkohler Number ( b)
Figure 5. Difference in amine and carboxyl end group concentrations (mmol/ll3 g) for the nylon 6,6 wiped film reactor model at a steam vapor pressure of 300 mmHg and Nmix= 50; (a) 270 "C, (b) 280 "C, (c) 290 "C, (d) 300 "C.
Figure 6. Concentration of cyclized end groups (mmol/ll3 g) for the nylon 6,6 wiped film reactor model at a steam vapor pressure of 300 mmHg and N,, = 50; (a) 270 "C, (b) 280 "C, (c) 290 "C, (d) 300 "C.
monofunctional compounds and cyclization). The kinetic constants for the cyclization reaction, the levels of monofunctional compounds, and the reactor temperatures they chose to investigate explain their observations. Molecular weight is not the only important product property for industrial quality nylon 6,6. For example, fibers must also often have the proper balance of end groups for good dyeability and very small amounts of gelled material for fiber spinning. In the absence of degradation reactions, the number of end groups a t a given molecular weight can be calculated and there are an equal number of amine and carboxyl ends. In an industrial nylon 6,6 with a molecular weight of 20000 g/mol, there are about 6 mmol/ll3 g of amine and carboxyl end groups. The difference in the amine and carboxyl end groups for typical operating conditions is shown in Figure 5a. Even a t a temperature of 280 "C, the side reactions are present in appreciable amounts, giving rise to a difference of up to 1.0 mmol/ll3 g in the end groups. As the temperature is increased to 300 "C, the maximum difference in chain ends increases to 3.7. Our calculations show that the difference in end groups approximately doubles with every 10 "C increase in temperature from 270 to 300 "C. The most striking feature of Figure 5 other than the sharp increase in the difference in chain ends is that the results are nearly independent of mass-transfer effects (e.g., film thickness or Thiele modulus). Kumar et al. (1984) report a similar result for the amount of cyclic material found in PET. It is also possible to understand why the molecular weight begins to level off at 300 "C (see Figure 4c) at longer residence times. The difference in chain ends
is nearly one-half the total number of chain ends, and this large stoichiometric imbalance is limiting the amount of amidation that can take place. The majority of stabilized chain ends that are inactive and can not undergo amidation are cyclized ends. The concentrations of cyclized ends for the same operating conditions as Figure 5 are shown in Figure 6. Similar overall trends emerge for the cyclized end group concentration; they are present a t low temperatures, although their production increases very sharply with increasing temperature and is insensitive to the rate of mass transfer. However, the concentration of cyclized ends is always higher than the difference in amine and carboxyl end group concentrations. Since a comprehensive kinetic model including degradation is not always available for most polymerizations, it is important to compare the predictions above for the wiped film reactor model in the absence of degradation reactions. Figure 7 shows the predictions without degradation effects for a typical set of operating conditions. This should be compared to the predictions of the model with degradation for the same operating conditions in Figure 2c. At smaller residence times (Damkohler numbers less than 1.51, the two models are similar; however, at larger residence times, the predictions of molecular weight for the model without degradation are significantly larger. The highest molecular weight predicted without degradation is over 19 000 g/mol, whereas the prediction with degradation is just over 17 000 g/mol. This is consistent with the increase in degradation products shown in Figures 5b and 6b.
2018 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
0.10 0.65 1.25 1.54 2.42 3.00
Damkohler Number (8)
0 10
0.65
125
154
242
300
Damkohler Number
Figure 7. Number-average molecular weight predictions for the nylon 6,6 wiped film reactor model neglecting degradation reactions at 280 "C, Nmix= 50, and 300 mmHg steam vapor pressure.
These results are in contrast to those of Ravindranath and Mashelkar (1984), who found that PET degradation reactions increased the rate of molecular weight generation. These differences can only be explained by looking more closely at the degradation mechanisms and reaction rates for the two systems. In their P E T polycondensation model, degradation reactions form reactive carboxylic acid end groups that participate in the condensation reaction (they react with hydroxyl end groups). Polycondensation via this mechanim is much faster than the usual ester interchange route. Although the possibility of similar behavior does exist in our degradation scheme, as reaction 1.4 does build the molecular weight, our kinetic parameters would have to be wrong by many orders of magnitude for this to occur. Generally, reactions 1.1and 1.2 are the most prevalent degradation reactions, they lead to a stoichiometric imbalance and decreased molecular weight generation, and their stabilized end group byproduct is much less reactive. The wiped film polymerizer effluent is not at equilibrium and continues to polymerize with further processing (e.g., in transfer lines and processing equipment). Peebles and Huffman (1971) showed that the degradation behavior of nylon 6,6 was drastically altered if the degradation took place in a closed reactor where the gaseous products were maintained over the melt compared with an open reactor (nitrogen atmosphere). The degradation scheme we are employing is only applicable to open reactors. We may turn off the degradation reactions and calculate the equilibrium molecular weight that may be reached in a closed reactor (transfer line). This has been done in Figure 8a, which should be compared with Figure 2c, which is the initial condition for Figure 8a. A significant increase in molecular weight will occur if the reactor effluent is kept in a heated transfer line for approximately 20-40 min without significant degradation. We expect that Figure 8a represents an upper bound on the attainable molecular weight, as it has been calculated by ignoring the degradation that would probably consume end groups and lead to a lowering of the molecular weight. Similar results for the same operating temperature and degree of mixing but for a lower pressure are shown in Figure 8b, which should be compared to Figure 3a; even more drastic increases in the molecular weight are possible. The ultimate molecular weight (Figure 8a,b) is more highly dependent on the film thickness (Thiele modulus) than on the reactor outlet molecular weight (Figures 2c and 3a). However, as the temperature is increased to 300 "C, at a steam pressure of 300 mmHg, and at Nmix of 50, the in-
v)
=
10.0 8.9 7.0 6.7 5.6
2 4.5
E
3.4 2.3 1.2 n -. .i 0.10 0.65 1.25 1.54 2.42 3.00
Damkohler Number (b) 10.0 1 8.9
Y
7.0
::;
P 4.5
*E
3.4
2.3 1.2 n -. i, 0.10 0.65 1.25 1.54 2.42 3.00
Damkohler Number (C)
Figure 8. Ultimate number-average molecular weight predictions for the nylon 6,6 wiped film reactor model for N- = 50; (a) T = 280 "C, P = 300 mmHg; (b) T = 280 "C,P = 100 mmHg; (c) T = 300 O C , P = 300 mmHg.
crease in ultimate molecular weight is reduced as shown in Figure 8c (cf., Figure 4c); this can be attributed to the difference in reactive chain ends for the amidation reaction and the proliferation of unreactive chain ends (see Figures 5d and 6d). Since the ratio of the Thiele modulus to the Damkohler number is independent of the reaction time (see eqs 8 and 9, we can interpret an increase of the Thiele modulus with @ 2 / D aheld constant as a larger reactivity of the main amidation reaction, e.g., increasing the catalyst activity. The effect of a catalyst on the molecular weight is shown in Figure 9a for a reactor temperature of 280 O C , steam pressure of 300 mmHg, and Nmix of 50. The molecular weight is increased significantly a t all values of the ratio @ / D a . Large ratios correspond to short reactors (small residence times) and thicker films (longer diffusion times); the increase in the molecular weight due to a more active catalyst is significant. However, at low values of the ratio, which correspond to long reactors (long residence times) and thinner films (shorter diffusion times), the increase in molecular weight is much greater. Thus, when the reactor is operating under reaction control, the effect of a more active catalyst is much greater than when the reactor operates closer to diffusion control. This fact is emphasized in Figure 9b, which was calculated under a no-mixing operating condition, and therefore, the reactor
Ind. Eng. Chem. Res., Vol. 29, No. 10,1990 2019 COz = carbon dioxide D = diffusivity, cm2/s Da = Damkohler number (k'&&/ ( V y ) ) dimensionless , Eapp= apparent activation energy, cal/mol H = film height, cm k . = forward reaction rate constant for reaction i, h-I kb = reference apparent forward reaction rate constant, 2.926
10.0 8.9
7.0
-%
6.7 5.6
.t
ag-l
4.5 3.4 2.3 1.2 0.1 0.10
0.65
1.25 1.54 2.42 Thiele McduludDa
3.00
(8)
1
E,, = apparent equilibrium constant (XLXw/XAXc), dimensionless L = amide linkage or reactor length, m M,, = number-average molecular weight, g/mol NH3 = ammonia ri = reaction rate, dimensionless Ri = reaction rate of component i, mol/(L h) SB = Schiff base end group SE = stabilized or cyclized end group t = time, dimensionless u y = velocity, dimensionless ( u y ) = average velocity, m/h W = water molecule, eq 1 x = binary mole fraction of water (Ci/c), dimensionless, Xi = mole fraction of component i for nylon 6,6 amidation (Ci/CT), dimensionless X = cross-link compound X = coordinate direction for reactor width, dimensionless Y = coordinate direction through the reactor, dimensionless Z = coordinate direction across the film, dimensionless Greeks @ = Thiele modulus (Wk$,/D), dimensionless
0.10
0.65
1.25 1.54 2.42 Thiele ModuludDa
3.00
(b)
Figure 9. Number-average molecular weight predictions for the nylon 6,6wiped film reactor model at 280 "C and 300 mmHg steam vapor pressure; (a) Nmix= 50, (b) Nmix = 1.
operates closer to diffusion control. Conclusions Small amounts of mixing significantly improve the mass transfer and increase the molecular weight generation in the wiped film polymerization reactor for all but the thinnest films. In addition, increasing the polymerization temperature beyond 285 "C adversely affects the product quality through degradation reactions. These degradation reactions lead to a stoichiometric imbalance, which eventually limits further increases in the molecular weight. In fact, the molecular weight can even go through a maximum in the reactor and the polymer begins depolymerizing. Increasing the pressure lowers the maximum attainable molecular weight. A catalyst for the main amidation reaction could yield improved reactor performance at all but the lowest mixing rates. The effluent from the reactor is not a t equilibrium, and further increases in the molecular weight will be realized if the polymer is kept at elevated temperatures. Acknowledgment We are grateful for financial and technical support from E. I. du Pont de Nemours & Co. Nomenclature A = amine end group I:= carboxyl end group C = molar density (Cw + Cp), dimensionless Ci = concentration of component i, dimensionless CT = total molar density for nylon 6,6 amidation (CT = CA Cc + CL+ Cw + CsE + CSB+ Cx),dimensionless (before eq 5, mol/L)
Registry No. PET, 25038-59-9; nylon 66, 32131-17-2.
Literature Cited Amon, M.; Denson, C. D. Simplified Analysis of the Performance of Wiped-Film Polycondensation Reactors. Ind. Eng. Chem. Fundam. 1980,19, 415. Amon, M.; Denson, C. D. Ind. Eng. Chem. Fundam. 1983,22,268. Ault, J. W.; Mellichamp, D. a. A Diffusion and Reaction Model for Simple Polycondensation. Chem. Eng. Sci. 1972a,27, 1441. Ault, J. W.; Mellichamp, D. A. Complex linear polycondensation-I Semi-batch reactor. Chem. Eng. Sci. 1972b,27,2219. Ault, J. W.; Mellichamp, D. A. Complex linear polycondensation-I1 Polymerization rate enhancement in thick film reactors. Chem. Eng. Sci. 1972c,27,2233. Costa, M. R. N. Fundamentals of the Modeling of Reversible Linear Polycondensations, Conceptual and for the Use of Industrial Processes. Ph.D. Thesis, Institut National Polytechnique de Lorraine, France, 1983. Flory, P. J. Principles of Polymer Chemistry; Cornel1 University Press: Ithaca, NY, 1953. Gupta, S. K.; Kumar, A.; Ghosh, A. K. Simulation of Reversible AA + B'B" Polycondensations in Wiped Film Reactors. J . Appl. Polym. Sci. 1983,28,1063. Kumar, A.; Gupta, S. K.; Madan, S.; Shah, N. G.; Gupta, S. K. Solution of Final Stages of Polyethylene Terephthalate Reactors Using Orthogonal Collocation Technique. Polym. Eng. Sci. 1984, 24, 194. Lin, K.-H.; Van Ness, H. C. Reaction Kinetics, Reactor Design, And Thermodynamics. In Chemical Engineers' Handbook; Perry, R. H., Chilton, C. H., Eds.; McGraw-Hill: New York, 1973; Chapter 4. Nagasubramanian, K.; Reimschuessel, H. K. Diffusion of Water and Caprolactam in Nylon 6 Melts. J . Appl. Polym. Sci. 1973,17, 1663.
Newitt, D. M.; Weale, K. E. Soluion and Diffusion of Gases in Polystyrene at High Pressure. J . Chem. SOC.1948,1541. Ogata, N. Studies on Polycondensation Reactions of Nylon Salt I. The Equilibrium in the System of Polyhexamethylene Adipamide and Water. Die Makromol. Chem. 1960,42,52. Peebles, L.H.; Huffman, M. W. Thermal Degradation of Nylon 66. J.Polym. Sci. 1971,9, 1807. Press, W. H.; Flannery, B. P.; Teukolsky, S. A,; Vetterling, W. T. Numerical Recipes: The Art of Scientific Computing;Cambridge University Press: New York, 1986; Chapter 17.
2020
Ind. Eng. Chem. Res. 1990,29, 2020-2023
Ravindranath, K.; Mashelkar, R. A. Finishing Stages of P E T Synthesis: A Comprehensive Model. AIChE J. 1984, 30, 415. Roos, J. P. Adv. Chem. Ser. 1974, 133, 303. Smith, J. M. Chemical Engineering Kinetics, 2nd ed.; McGraw Hill: New York, 1970; Chapter 11. Steppan, D. D.; Doherty, M. F.; Malone, M. F. A Kinetic and Equilibrium Model for Nylon 6,6 Polymerization. J . Appl. Polym. Sci. 1987, 33, 2333. Steppan, D. D.; Doherty, M. F.; Malone, M. F. A Flowing Film Model for Nylon 6,6 Polymerization. Ind. Eng. Chem. Res. 1989, 28, 1324.
Steppan D. D.; Doherty, M. F.; Malone, M. F. Film Diffusion Effects in Nylon 6,6 Polymerization. J . Appl. Polym. Sci. 1990a, in press. Steppan, D. D.; Doherty, M. F.; Malone, M. F. A Simplified Degradation Model for Nylon 6,6 Polymerization. J . Appl. Polym. Sci. 1990b, in press. US.Patent 3,900,450,Du Pont, 1975; Preparation of Polyamides by Continuous Polymerization. Received for review October 11, 1989 Revised manuscript received May 10, 1990 Accepted May 23, 1990
Lanthanum-NaY Zeolite Ion Exchange. 1. Thermodynamics and Thermochemistry Shiann-Horng Chen,+Kuei-Jung Chao,*ptand Ting-Yueh Leet Departments of Chemistry and Chemical Engineering, National Tsinghua University, Hsinchu, Taiwan, Republic of China
T h e lanthanum ion exchange isotherms for NaY a t 27 and 60 "C were obtained and analyzed. Thermodynamic parameters were calculated by assuming that the cation exchanger has two groups of sites in supercages. Crystalline aluminosilicate zeolites are widely used as sorbents, shape-selective catalysts, and cation exchangers because of their special crystal structure and their negatively charged tetrahedral framework. The rare-earth (RE) forms of zeolite Y obtained by ion exchange of synthetic NaY with RE ions are important catalysts in petroleumrefining processing (Venuto and Habib, 1979; Poustma, 1976). However, little is published on the thermodynamic properties of RE-NaY ion exchange reactions. In zeolite Y, cations are located in their supercage, sodalite, and double hexagonal prism cavities. Sherry (1969, 1976) reported that, because of its large size, a hydrated La3+ion cannot migrate from a supercage to a small sodalite cage to replace the residing Na+ ions, and the La-NaY ion exchange reaction terminates at an exchange level of 0.69 f 0.01 at 25 "C. Unless the temperature of exchange is raised above 82 or 100 "C, the La3+ions can only replace Na+ ions in the supercages (Reng and Chen, 1980; Bennett and Smith, 1969). Moreover, the isotherms for RE3+-Na+ exchange are expected to be reversible only when the Na+ ions in the supercage have been replaced at low reaction temperatures. Using the Gaines and Thomas (1953) thermodynamic formulation and graphical method (Dyer et al., 19811, Rees and Zuyi (1986) calculated the thermodynamic properties of the entire RE-NaY ion exchange reaction at 25 and 65 "C. Furthermore, radiochemical results (Dyer and Ogden, 1974) showed that roughly half of the Na+ ions in NaY are easily exchanged by Ce3+ions, a further one-fifth are more difficult to exchange, and the remaining Na+ ions are most difficult to exchange. It is believed that the framework of Y zeolites may provide several groups of cationic sites associated with their distinct intracrystalline environments. In this work, La-NaY exchange isotherms at 27 and 60 "C were measured and analyzed by assuming that the cation exchanger has several groups of sites (Barrer et al., 1973; Barrer and Klinowski, 1978). The modified Lang-
* To whom correspondence should be addressed. 'Department of Chemistry. Department of Chemical Engineering.
*
muir adsorption model was found to satisfactorily simulate the La-NaY ion exchange equilibrium.
Experimental Section The binder-free NaY zeolite was obtained from Strem Chemical Company. The zeolite was washed with 1 N NaCl solution and with deionized water. The washed samples were dried a t room temperature and stored for at least 2 days in a desiccator containing saturated NHICl solution. The NaY zeolite was decomposed in a pressure bomb with mixed acids, HC1-HN03-HF, and analyzed by inductively coupled plasma atomic emission spectrometry (ICP-AES). The atomic ratios of Na/A1 and Si/Al in NaY were 0.99 f 0.01 and 2.29 f 0.03, respectively. The composition of the anhydrous NaY sample is Na58,s(A102)58.3(Si02),33.7. The reagent-grade LaCl, (E. Merck) was mixed with deionized water to prepare 0.1 equiv/L solutions. The La-NaY ion exchange reaction was carried out by weighing suitable quantities of the NaY zeolite in 125-mL polypropylene bottles containing 100 mL of the salt solution and letting the system equilibrate in a water bath shaker at 27 or 60 "C. After 3-5 days of contact time between zeolite and solution, the concentrations of the cations in the solution were found to be constant, but it was found by Rees and Zuyi (1986) that the reversibility of the LaNaY ion exchange isotherm can be established at an equilibration time of about 1 week for each measurement at 25-65 "C. Therefore, the equilibrations of ion exchange reported in this paper were carried out in sealed plastic bottles for 7-10 days. Immediately after being removed from the constant-temperature bath, the solid and solution phases in equilibrium were rapidly separated by filtration through a Millipore membrane filter. The solid was washed with deionized water, dried at room temperature, and stored in a desiccator containing saturated NH4C1 solution. It was later decomposed with HC1-HN03-HF mixed acids. The solid and the solution phases in equilibrium were analyzed by ICP-AES. The degree of exchange was estimated both from the La/A1 and Na/A1 molar ratios in the solid phase and from the Na and La
0888-5885/90/2629-2020$02.50/0 0 1990 American Chemical Society
